How to Build Knowledge in Geometry

     This week in my mathematics education I learned more about how to be an effective teacher of geometry to my students. For many students geometry is a difficult part of math, but is obviously essential to our everyday life. I believe that teachers can demonstrate the importance of geometry by showing them how it applies to our everyday life. This can be done by asking relatable questions for students to solve in order to see how the knowledge they have gained will benefit them later in life. However, these questions must be easy enough so every student can begin the task, but hard enough so it is challenging to all students. As the capacity building series article states, questions must be an effective means to deeper a student’s understanding, but cannot interfere with their method of learning the topic on their own.  As I attend my observation days at my placement school I realize the difficulty in this, but also the reward that comes when students get excited about completing a problem.

     This week also demonstrated to me how math can be made interesting if the right tools are used. For example, we used a Halloween theme to have a discussion on similar and congruent shapes, and the meaning of each term. This is an effective method because students will remember the lesson by the images they saw. Another example that was displayed was the reading of a children’s book on geometry called The Greedy Triangle. Here the students read about an interesting story about a triangle who continuously asked for more sides, thereby creating a new shape. The book is an effective example of how students can learn without even knowing it because they are so interested in what they are reading. Unfortunately when I was a student I do not remember my math teachers engaging my classmates and me through these sorts of fun ideas, especially as I moved up in grade levels. As a result, I became disinterested in math as it was just about boring lessons and textbook homework. I believe that teachers need to make an effort to make mathematics fun to their students. Not only will they see students who are more engaged, but also students who retain the material much better.

     The final main idea that I learned this week was that a topic like geometry needs to be taught using manipulatives. Students need to be able to physically interact with the shapes they are learning about whether it is through block tens or tangrams or whichever you choose. Here students can deepen their understanding by being able to visualize what they are learning, but are also developing other parts of their brain in the process. This is an effective way that teachers can engage students who learn in different ways and provides them the opportunity to work with the manipulatives that best suits them. This could be done through discussion or playing with the blocks or laying all the blocks and visualize in your head. Overall, it is clear that students gain a deeper learning when they are given the chance to explore. Here students can gain a relational understanding, instead of the instrumental understanding which has been emphasized far too much.